Introduction to Hadronic Final State Reconstruction in Collider Experiments (Part IV)

Intr

oduc

tion

to

Had

roni

c Fi

nal S

tate

Re

cons

truc

tion

in C

ollid

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xper

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ts

Introduction to Hadronic Final State Reconstruction in Collider Experiments

(Part IV)

Peter LochUniversity of Arizona

Tucson, ArizonaUSA

2P. Loch

U of ArizonaFebruary 18, 2010

Calorimeter Response

What is response? Reconstructed calorimeter signal

Based on the direct measurement – the raw signal

May include noise suppression Has the concept of signal (or energy)

scale Mostly understood as the basic signal

before final calibrations Does not explicitly include particle or

jet hypothesis Uses only calorimeter signal amplitudes,

spatial distributions, etc.

current in gap(nA)

shaper output(mV)

digitized samples

(ADC cts)

transmission line, pre-amplifier, shaper

digitization, gain selection

digital filter, electronic calibration, corrections

energy Eraw (MeV)time t (ns)quality Qselected gain gonline id idonline

Raw Channel Data

electronic and effi

cu

ci

rren

ency

t calibr

correct

energy cal

atio

ibratio

i s

n

on

n

ADC nA

HV cross-talk purit

nA MeV

y

raw peakE A

3P. Loch

U of ArizonaFebruary 18, 2010

Calorimeter Signal in ATLAS

Slow signal collection in liquid argon calorimeters ~450 ns @ 1 kV/mm drift time

versus 40 MHz/25 ns bunch crossing time Measure only I0 = I(t0) (integrate

<25 ns) Applying a fast bi-polar signal

shaping Shaping time ~15 ns

With well known shape Shaped pulse integral = 0

Net average signal contribution from pile-up = 0

Need to measure the pulse shape (time sampled readout)

Total integration ~25 bunch crossings 23 before signal, 1 signal, 1 after

signal

reading out (digitize) 5 samples sufficient!

4P. Loch

U of ArizonaFebruary 18, 2010

ATLAS Digital Filtering

What is digital filtering Unfolds the expected (theoretical) pulse

shape from a measured pulse shape Determines signal amplitude and timing

Minimizes noise contributions Noise reduced by ~1.4 compared to single

reading Note: noise depends on the luminosity

Requires explicit knowledge of pulse shape Folds triangular pulse with transmission

line characteristics and active electronic signal shaping

Characterized by signal transfer functions depending on R, L, C of readout electronics, transmission lines

Filter coefficients from calibration system Pulse “ramps” for response

Inject known currents into electronic chain

Use output signal to constrain coefficients Noise for auto-correlation

Signal history couples fluctuations in time sampled readings

s

s

peak1

pe

peak

pea

ak pea

k

k1

Signal amplitude (energy):

digital filter coefficient , with reading in time sample

pedestal readingSignal peak time :

iN

i i ii

N

i ii

aA a s p s

p

A t b

t

s

A

p

W.E. Cleland and E.G. Stern, Nucl. Inst. Meth. A338 (1994) 467.

5P. Loch

U of ArizonaFebruary 18, 2010

ATLAS Digital Filtering

What is digital filtering Unfolds the expected (theoretical) pulse

shape from a measured pulse shape Determines signal amplitude and timing

Minimizes noise contributions Noise reduced by ~1.4 compared to single

reading Note: noise depends on the luminosity

Requires explicit knowledge of pulse shape Folds triangular pulse with transmission

line characteristics and active electronic signal shaping

Characterized by signal transfer functions depending on R, L, C of readout electronics, transmission lines

Filter coefficients from calibration system Pulse “ramps” for response

Inject known currents into electronic chain

Use output signal to constrain coefficients Noise for auto-correlation

Signal history couples fluctuations in time sampled readings

s

s

peak1

pe

peak

pea

ak pea

k

k1

Signal amplitude (energy):

digital filter coefficient , with reading in time sample

pedestal readingSignal peak time :

iN

i i ii

N

i ii

aA a s p s

p

A t b

t

s

A

p

s

s

1

1

Constraints for digital filter coefficients :

1 , w

normalized physics p

ith bein

ulse shap

0

e

g the

iN

i ii

Ni

i

ii

g

a

ag

gat

W.E. Cleland and E.G. Stern, Nucl. Inst. Meth. A338 (1994) 467.

6P. Loch

U of ArizonaFebruary 18, 2010

ATLAS Digital Filter Coefficients

7P. Loch

U of ArizonaFebruary 18, 2010

Calorimeter Response

What does signal or energy scale mean? Indicates a certain level of signal

reconstruction Standard reconstruction often stops with a

basic signal scale Electromagnetic energy scale is a good

reference Uses direct signal proportionality to

electron/photon energy Accessible in test beam experiments Can be validated with isolated particles in

collision environment Provides good platform for data and

simulation comparisons Does not necessarily convert the electron

signal to the true photon/electron energy! Hadronic signals can also be calculated on

this scale Good platform for comparisons to

simulations But does not return a good estimate for the

deposited energy in non-compensating calorimeters – see later discussion!

Is not a fundamental concept of physics! Is a calorimeter feature Definition varies from experiment to

experiment

active

vis 0

emrec e 0

0

e

!vis vis

e vis depdep 0 e

e

Recall electrons/photons in sampling calorimeters:

Electron sampling fraction relates signal and deposited energy:

1

with

d

E N N E

E c A

dE dx Edx

S

E ES E E EE E S

c

emdep rec e

e e

being the electron calibration constant.( is a unitless fraction, converts a signal unitinto an energy unit, e.g. nA MeV)

Response oft ( )en denoted ( , )

S c

e e E E c A

8P. Loch

U of ArizonaFebruary 18, 2010

Hadronic Response (1)

D.Groom et al., NIM A338, 336-347 (1994)

0 em 0 em 0

em 0

em 0 em 0

Single hadron reponse:( ) ( ) 1 ( )

( ) intrinsic em fractionwith response of pure

hadronic shower branch Non-compensation measure:

1( ) 1 ( )

E f E e f E h

f E

h

f Ee

ef E h

1em 0 0 base

base

Popular parametrization by Groom et al.:

( ) 1

1.0 GeV for 0.80 0.85,

2.6 GeV for

mf E E E

m Ep

9P. Loch

U of ArizonaFebruary 18, 2010

Hadronic Response (2)

Observable

provides experimental access to characteristic calorimeter variables in pion test beams by fitting h/e, Ebase and m from the energy dependence of the pion signal on electromagnetic energy scale:

Note that e/h is often constant, for example: in both H1 and ATLAS about 50% of the energy in the hadronic branch generates a signal independent of the energy itself

2.6e h

1 10 base 0 base

10 base

1

11 1

m m

m

e e

E E h E E e

h e E E

dep0em emrec rec( ) ( )

EEeE E

10P. Loch

U of ArizonaFebruary 18, 2010

Jet Response

Complex mixture of hadrons and photons Not a single particle response Carries initial electromagnetic

energy Mainly photons

Very simple response model Assume the hadronic jet content is

represented by 1 particle only Not realistic, but helpful to

understand basic response features

More evolved model Use fragmentation function in jet

response This has some practical

considerations E.g. jet calibration in CDF

Gets non-compensation effect Does not address acceptance effect

due to shower overlaps

11P. Loch

U of ArizonaFebruary 18, 2010

Jet Response

Complex mixture of hadrons and photons Not a single particle response Carries initial electromagnetic

energy Mainly photons

Very simple response model Assume the hadronic jet content is

represented by 1 particle only Not realistic, but helpful to

understand basic response features

More evolved model Use fragmentation function in jet

response This has some practical

considerations E.g. jet calibration in CDF

Gets non-compensation effect Does not address acceptance effect

due to shower overlaps

jet jet jetem em

had had jetem em jet jet jet

1hadjet

embase

( )1 1

( ), 1

[single particle approximation]

1

[Groom's parameterization]

m

j E hff ffe e

ff E E f E

Ef

E

12P. Loch

U of ArizonaFebruary 18, 2010

Jet Response

Complex mixture of hadrons and photons Not a single particle response Carries initial electromagnetic

energy Mainly photons

Very simple response model Assume the hadronic jet content is

represented by 1 particle only Not realistic, but helpful to

understand basic response features

More evolved model Use fragmentation function in jet

response This has some practical

considerations E.g. jet calibration in CDF

Gets non-compensation effect Does not address acceptance effect

due to shower overlaps

Energy (GeV)

Resp

onse

Rat

io

( )E e( )j E e

( ) ( )j E E

13P. Loch

U of ArizonaFebruary 18, 2010

Jet Response

Complex mixture of hadrons and photons Not a single particle response Carries initial electromagnetic

energy Mainly photons

Very simple response model Assume the hadronic jet content is

represented by 1 particle only Not realistic, but helpful to

understand basic response features

More evolved model Use fragmentation function in jet

response This has some practical

considerations E.g. jet calibration in CDF

Gets non-compensation effect Does not address acceptance effect

due to shower overlaps

em had em had hadhadrons

composition of hadronic component given by jet fragmentation funct

jet

jet

jet

1

jet had

io

jet

had

bas

n

e

( ) 1 ( )

( )

1

1 1m

hf E f E d

j Eef

f

f

E EE

E

fE

e

1je

1

hadro

t jethad bas

ns b

ehad

s

o

e

r

a

ns

1 1 1

m

mff E E h

h e

e

14P. Loch

U of ArizonaFebruary 18, 2010

Acceptance and Noise in Jet Response

Noise Fluctuations of the “zero” or “empty” signal

reading Pedestal fluctuations

Independent of the signal from particles At least to first order

Mostly incoherent No noise correlations between readout

channels Noise in each channel is independent

oscillator

Gaussian in nature Pedestal fluctuations ideally follow normal

distribution around 0 Width of distribution (1 σ) is noise value

Signal significance Noise can fake particle signals

Only signals exceeding noise can be reliably measured

Signals larger than 3 × noise are very likely from particles

Gaussian interpretation of pedestal fluctuations Calorimeter signal reconstruction aims to

suppress noise Average contribution = 0, but adds to

fluctuations!

Small signal: Noise only Signal on top of noise Sum of noise and signal Signal after noise suppression

noiseReading ( )

Spatial Coordinate/Calorimeter Cell

15P. Loch

U of ArizonaFebruary 18, 2010

Acceptance and Noise in Jet Response

Noise Fluctuations of the “zero” or “empty” signal

reading Pedestal fluctuations

Independent of the signal from particles At least to first order

Mostly incoherent No noise correlations between readout

channels Noise in each channel is independent

oscillator

Gaussian in nature Pedestal fluctuations ideally follow normal

distribution around 0 Width of distribution (1 σ) is noise value

Signal significance Noise can fake particle signals

Only signals exceeding noise can be reliably measured

Signals larger than 3 × noise are very likely from particles

Gaussian interpretation of pedestal fluctuations Calorimeter signal reconstruction aims to

suppress noise Average contribution = 0, but adds to

fluctuations!

Small signal: Noise only Signal on top of noise Sum of noise and signal Signal after noise suppression

noiseReading ( )

Spatial Coordinate/Calorimeter Cell

16P. Loch

U of ArizonaFebruary 18, 2010

Acceptance and Noise in Jet Response

Noise Fluctuations of the “zero” or “empty” signal

reading Pedestal fluctuations

Independent of the signal from particles At least to first order

Mostly incoherent No noise correlations between readout

channels Noise in each channel is independent

oscillator

Gaussian in nature Pedestal fluctuations ideally follow normal

distribution around 0 Width of distribution (1 σ) is noise value

Signal significance Noise can fake particle signals

Only signals exceeding noise can be reliably measured

Signals larger than 3 × noise are very likely from particles

Gaussian interpretation of pedestal fluctuations Calorimeter signal reconstruction aims to

suppress noise Average contribution = 0, but adds to

fluctuations!

Small signal: Noise only Signal on top of noise Sum of noise and signal Signal after noise suppression

noiseReading ( )

Spatial Coordinate/Calorimeter Cell

17P. Loch

U of ArizonaFebruary 18, 2010

Acceptance and Noise in Jet Response

Noise Fluctuations of the “zero” or “empty” signal

reading Pedestal fluctuations

Independent of the signal from particles At least to first order

Mostly incoherent No noise correlations between readout

channels Noise in each channel is independent

oscillator

Gaussian in nature Pedestal fluctuations ideally follow normal

distribution around 0 Width of distribution (1 σ) is noise value

Signal significance Noise can fake particle signals

Only signals exceeding noise can be reliably measured

Signals larger than 3 × noise are very likely from particles

Gaussian interpretation of pedestal fluctuations Calorimeter signal reconstruction aims to

suppress noise Average contribution = 0, but adds to

fluctuations!

Small signal: Noise only Signal on top of noise Sum of noise and signal Signal after noise suppression

noiseReading ( )

Spatial Coordinate/Calorimeter Cell

18P. Loch

U of ArizonaFebruary 18, 2010

Acceptance and Noise in Jet Response

Noise Fluctuations of the “zero” or “empty” signal

reading Pedestal fluctuations

Independent of the signal from particles At least to first order

Mostly incoherent No noise correlations between readout

channels Noise in each channel is independent

oscillator

Gaussian in nature Pedestal fluctuations ideally follow normal

distribution around 0 Width of distribution (1 σ) is noise value

Signal significance Noise can fake particle signals

Only signals exceeding noise can be reliably measured

Signals larger than 3 × noise are very likely from particles

Gaussian interpretation of pedestal fluctuations Calorimeter signal reconstruction aims to

suppress noise Average contribution = 0, but adds to

fluctuations!

Large signal: Noise only Signal on top of noise Sum of noise and signal Signal after noise suppression

noiseReading ( )

Spatial Coordinate/Calorimeter Cell

19P. Loch

U of ArizonaFebruary 18, 2010

Acceptance and Noise in Jet Response

Noise Fluctuations of the “zero” or “empty” signal

reading Pedestal fluctuations

Independent of the signal from particles At least to first order

Mostly incoherent No noise correlations between readout

channels Noise in each channel is independent

oscillator

Gaussian in nature Pedestal fluctuations ideally follow normal

distribution around 0 Width of distribution (1 σ) is noise value

Signal significance Noise can fake particle signals

Only signals exceeding noise can be reliably measured

Signals larger than 3 × noise are very likely from particles

Gaussian interpretation of pedestal fluctuations Calorimeter signal reconstruction aims to

suppress noise Average contribution = 0, but adds to

fluctuations!

Large signal: Noise only Signal on top of noise Sum of noise and signal Signal after noise suppression

noiseReading ( )

Spatial Coordinate/Calorimeter Cell

20P. Loch

U of ArizonaFebruary 18, 2010

Acceptance and Noise in Jet Response

Noise Fluctuations of the “zero” or “empty” signal

reading Pedestal fluctuations

Independent of the signal from particles At least to first order

Mostly incoherent No noise correlations between readout

channels Noise in each channel is independent

oscillator

Gaussian in nature Pedestal fluctuations ideally follow normal

distribution around 0 Width of distribution (1 σ) is noise value

Signal significance Noise can fake particle signals

Only signals exceeding noise can be reliably measured

Signals larger than 3 × noise are very likely from particles

Gaussian interpretation of pedestal fluctuations Calorimeter signal reconstruction aims to

suppress noise Average contribution = 0, but adds to

fluctuations!

Large signal: Noise only Signal on top of noise Sum of noise and signal Signal after noise suppression

noiseReading ( )

Spatial Coordinate/Calorimeter Cell

21P. Loch

U of ArizonaFebruary 18, 2010

Acceptance and Noise in Jet Response

Noise Fluctuations of the “zero” or “empty” signal

reading Pedestal fluctuations

Independent of the signal from particles At least to first order

Mostly incoherent No noise correlations between readout

channels Noise in each channel is independent

oscillator

Gaussian in nature Pedestal fluctuations ideally follow normal

distribution around 0 Width of distribution (1 σ) is noise value

Signal significance Noise can fake particle signals

Only signals exceeding noise can be reliably measured

Signals larger than 3 × noise are very likely from particles

Gaussian interpretation of pedestal fluctuations Calorimeter signal reconstruction aims to

suppress noise Average contribution = 0, but adds to

fluctuations!

Large signal: Noise only Signal on top of noise Sum of noise and signal Signal after noise suppression

noiseReading ( )

Spatial Coordinate/Calorimeter Cell

22P. Loch

U of ArizonaFebruary 18, 2010

Acceptance and Noise in Jet Response

Noise Fluctuations of the “zero” or “empty” signal

reading Pedestal fluctuations

Independent of the signal from particles At least to first order

Mostly incoherent No noise correlations between readout

channels Noise in each channel is independent

oscillator

Gaussian in nature Pedestal fluctuations ideally follow normal

distribution around 0 Width of distribution (1 σ) is noise value

Signal significance Noise can fake particle signals

Only signals exceeding noise can be reliably measured

Signals larger than 3 × noise are very likely from particles

Gaussian interpretation of pedestal fluctuations Calorimeter signal reconstruction aims to

suppress noise Average contribution = 0, but adds to

fluctuations!

Large signal: Noise only Signal on top of noise Sum of noise and signal Signal after noise suppression

noiseReading ( )

Spatial Coordinate/Calorimeter Cell

calorimeter response < true signal!

23P. Loch

U of ArizonaFebruary 18, 2010

Acceptance and Noise in Jet Response

Noise Fluctuations of the “zero” or “empty” signal

reading Pedestal fluctuations

Independent of the signal from particles At least to first order

Mostly incoherent No noise correlations between readout

channels Noise in each channel is independent

oscillator

Gaussian in nature Pedestal fluctuations ideally follow normal

distribution around 0 Width of distribution (1 σ) is noise value

Signal significance Noise can fake particle signals

Only signals exceeding noise can be reliably measured

Signals larger than 3 × noise are very likely from particles

Gaussian interpretation of pedestal fluctuations Calorimeter signal reconstruction aims to

suppress noise Average contribution = 0, but adds to

fluctuations!

Small signal, two particles: Noise only Signal on top of noise Sum of noise and signal Signal after noise suppression

noiseReading ( )

Spatial Coordinate/Calorimeter Cell

24P. Loch

U of ArizonaFebruary 18, 2010

Acceptance and Noise in Jet Response

Noise Fluctuations of the “zero” or “empty” signal

reading Pedestal fluctuations

Independent of the signal from particles At least to first order

Mostly incoherent No noise correlations between readout

channels Noise in each channel is independent

oscillator

Gaussian in nature Pedestal fluctuations ideally follow normal

distribution around 0 Width of distribution (1 σ) is noise value

Signal significance Noise can fake particle signals

Only signals exceeding noise can be reliably measured

Signals larger than 3 × noise are very likely from particles

Gaussian interpretation of pedestal fluctuations Calorimeter signal reconstruction aims to

suppress noise Average contribution = 0, but adds to

fluctuations!

Small signal, first particle: Noise only Signal on top of noise Sum of noise and signal Signal after noise suppression

noiseReading ( )

Spatial Coordinate/Calorimeter Cell

25P. Loch

U of ArizonaFebruary 18, 2010

Acceptance and Noise in Jet Response

Noise Fluctuations of the “zero” or “empty” signal

reading Pedestal fluctuations

Independent of the signal from particles At least to first order

Mostly incoherent No noise correlations between readout

channels Noise in each channel is independent

oscillator

Gaussian in nature Pedestal fluctuations ideally follow normal

distribution around 0 Width of distribution (1 σ) is noise value

Signal significance Noise can fake particle signals

Only signals exceeding noise can be reliably measured

Signals larger than 3 × noise are very likely from particles

Gaussian interpretation of pedestal fluctuations Calorimeter signal reconstruction aims to

suppress noise Average contribution = 0, but adds to

fluctuations!

Small signal, first and second particle: Noise only Signal on top of noise Sum of noise and signal Signal after noise suppression

noiseReading ( )

Spatial Coordinate/Calorimeter Cell

26P. Loch

U of ArizonaFebruary 18, 2010

Acceptance and Noise in Jet Response

Noise Fluctuations of the “zero” or “empty” signal

reading Pedestal fluctuations

Independent of the signal from particles At least to first order

Mostly incoherent No noise correlations between readout

channels Noise in each channel is independent

oscillator

Gaussian in nature Pedestal fluctuations ideally follow normal

distribution around 0 Width of distribution (1 σ) is noise value

Signal significance Noise can fake particle signals

Only signals exceeding noise can be reliably measured

Signals larger than 3 × noise are very likely from particles

Gaussian interpretation of pedestal fluctuations Calorimeter signal reconstruction aims to

suppress noise Average contribution = 0, but adds to

fluctuations!

Small signal, two particle, sum: Noise only Signal on top of noise Sum of noise and signal Signal after noise suppression

noiseReading ( )

Spatial Coordinate/Calorimeter Cell

27P. Loch

U of ArizonaFebruary 18, 2010

Acceptance and Noise in Jet Response

Noise Fluctuations of the “zero” or “empty” signal

reading Pedestal fluctuations

Independent of the signal from particles At least to first order

Mostly incoherent No noise correlations between readout

channels Noise in each channel is independent

oscillator

Gaussian in nature Pedestal fluctuations ideally follow normal

distribution around 0 Width of distribution (1 σ) is noise value

Signal significance Noise can fake particle signals

Only signals exceeding noise can be reliably measured

Signals larger than 3 × noise are very likely from particles

Gaussian interpretation of pedestal fluctuations Calorimeter signal reconstruction aims to

suppress noise Average contribution = 0, but adds to

fluctuations!

Small signal, two particles: Noise only Signal on top of noise Sum of noise and signal Signal after noise suppression

noiseReading ( )

Spatial Coordinate/Calorimeter Cell

28P. Loch

U of ArizonaFebruary 18, 2010

Acceptance and Noise in Jet Response

Noise Fluctuations of the “zero” or “empty” signal

reading Pedestal fluctuations

Independent of the signal from particles At least to first order

Mostly incoherent No noise correlations between readout

channels Noise in each channel is independent

oscillator

Gaussian in nature Pedestal fluctuations ideally follow normal

distribution around 0 Width of distribution (1 σ) is noise value

Signal significance Noise can fake particle signals

Only signals exceeding noise can be reliably measured

Signals larger than 3 × noise are very likely from particles

Gaussian interpretation of pedestal fluctuations Calorimeter signal reconstruction aims to

suppress noise Average contribution = 0, but adds to

fluctuations!

Small signal, two particles: Noise only Signal on top of noise Sum of noise and signal Signal after noise suppression

noiseReading ( )

Spatial Coordinate/Calorimeter Cell

29P. Loch

U of ArizonaFebruary 18, 2010

Acceptance and Noise in Jet Response

Noise Fluctuations of the “zero” or “empty” signal

reading Pedestal fluctuations

Independent of the signal from particles At least to first order

Mostly incoherent No noise correlations between readout

channels Noise in each channel is independent

oscillator

Gaussian in nature Pedestal fluctuations ideally follow normal

distribution around 0 Width of distribution (1 σ) is noise value

Signal significance Noise can fake particle signals

Only signals exceeding noise can be reliably measured

Signals larger than 3 × noise are very likely from particles

Gaussian interpretation of pedestal fluctuations Calorimeter signal reconstruction aims to

suppress noise Average contribution = 0, but adds to

fluctuations!

Small signal, two particles: Noise only Signal on top of noise Sum of noise and signal Signal after noise suppression

noiseReading ( )

Spatial Coordinate/Calorimeter Cell

calorimeter response < true signal!